Closed hollow profiles are increasingly used in automotive engineering, which closed hollow profiles have cross sections and material thicknesses which are adapted specifically to the application. It is known to produce a closed hollow profile from two deep-drawn shells. To this end, the half shells, as described, for example, in German laid-open specification DE 41 20 404 A1, are first of all pre-formed and are subsequently calibrated in a post-forming step. It is problematical in the production of a hollow profile in this way that stresses are introduced into the blank during the deep-drawing operation, which stresses lead to springback of the half shells. The springback of the half shells makes it difficult, for example, to accurately position the half shells in a die for welding the half shells to form a closed hollow profile. Furthermore, half shells with pronounced springback cannot be used without additional work on account of the lack of dimensional accuracy. Various measures are known then from the prior art for avoiding a springback effect after the deep-drawing operation. A common feature of the measures known from the prior art, such as elongation of the component, provision of draw beads, partial hold-down control, tool adaptation measures or lubrication of the components, is that firstly complicated tools and drawing operations are used and secondly the stated measures show only limited success. Documents DE 10 2007 059 251 A1 and DE 10 2008 037 612 A1 have disclosed methods for producing half shells with low springback, the pre-formed half shell having excess material, with the result that the cross section is upset by way of a pressing operation to form the finished half shell during the forming of the preformed half shell into its finished shape. The stresses which are introduced into the blank material by way of the deep-drawing operation are oriented in this way, in order thus to counteract uncontrolled springback. In practice, however, the blanks do not always have a homogeneous thickness, as a result of which the material thickness of a half shell after the deep-drawing operation is subject to certain tolerances at least in the jacket region. By way of the above-described method, half shells which have the stated tolerances cannot be calibrated completely along their circumference, however. In particular in the region of the flange, if the latter is present, and in the region of the jacket, undesired corrugation formation occurs in the upset material during the upsetting operation, which corrugation formation firstly impairs the visual appearance of the half shell and secondly reduces the local dimensional accuracy. In addition, problems in the processing to form half shells with low springback can also arise on account of the springback of the pre-formed half shells and the associated lower dimensional accuracy of the pre-formed half shells. In the context of this application, the dimensional accuracy of a component is understood to mean a reduced tolerance in comparison with the conventional deep-drawing operation.